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Suppose we have a floating-rate bond with arbitrary face value.

I am given to understand that the value of such a bond is the face value, at the time it is issued and also after each coupon payment.

As an example, let the face value be 100, and let the interest rate at the time of issuance be 5%, so the coupon payment at the end of the first period is 5. Hence, the value of the bond is: $ \frac{(100 +5)}{1.05}=100$

A couple of things: 1. Why do we only consider the first period? Does this assume the bond is callable? 2. Do we assume the discount rate is the same as the floating rate?

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A floating rate bond is typically referencing to some interest rate curve (3m LIBOR, 6m EURIBOR etc.)

  1. You can also consider other periods, you just need to know the forward rate for that period, which is first derived from the interest rate curve and second discounted by that interest rate curve. This doesn't assume any embedded options.

  2. Only for the first period, since the first period forward rate is equal to the discount rate (after each coupon payment, you already know the next e.g. 3m LIBOR rate, which will be payed after 3 months).

HINT: the sum of the PV coupon payments over the entire life of the bond and the PV of the face value at maturity is equal to the face value today.

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  • $\begingroup$ Regarding 1., this doesn't lead to a PV that is the face value, does it? $\endgroup$
    – Student
    Commented May 30, 2020 at 12:49
  • $\begingroup$ It should, because the PV of the face value payment at maturity increases as it approaches the maturity date (the amout it increases is equal to the PV of the upcomming coupon payment). Regarding your example: the PV of the face value of 100 paid in e.g. 5 years is less than 100, the difference to 100 is exactly the PV of all coupon payments $\endgroup$
    – simzoor
    Commented May 30, 2020 at 12:55
  • $\begingroup$ Also, your Hint assumes the bond is trading at par when issued, right? $\endgroup$
    – Student
    Commented May 30, 2020 at 13:11
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    $\begingroup$ True, also absence of credit risk etc., tried to make the core issue as understandable as possible $\endgroup$
    – simzoor
    Commented May 30, 2020 at 13:43

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